Angie needs to have an annuity payment of $1,300 at the end of each year for the next 10 years. How much should she deposit now at 10% interest compounded annually, to yield this payment?

Booty

To find out how much Angie should deposit now to yield the desired annuity payment, you can use the formula for the present value of an annuity. The present value (PV) of an annuity is the lump sum amount that needs to be invested now to receive a series of future payments.

The formula for the present value of an ordinary annuity is:

PV = A * (1 - (1 + r)^(-n)) / r

Where:
PV = Present value
A = Annuity payment
r = Interest rate per period
n = Number of periods

In this case, Angie wants an annuity payment of $1,300 at the end of each year (A = $1,300), the interest rate is 10% (r = 0.10), and the annuity will last for 10 years (n = 10).

Substituting these values into the formula, we get:

PV = 1300 * (1 - (1 + 0.10)^(-10)) / 0.10

Now, let's calculate this:

PV = 1300 * (1 - (1.10)^(-10)) / 0.10
PV = 1300 * (1 - 0.386) / 0.10
PV = 1300 * 0.614 / 0.10
PV = 798.20

Therefore, Angie should deposit $798.20 now, at 10% interest compounded annually, to yield the desired annuity payment of $1,300 at the end of each year for the next 10 years.

FV * i/(1+i)^n - 1

81.57

1300*.10/(1+.10)^10-1

1300*.10/1.5937424601=

81.569013347265089909993043047244=
81.57